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Cannot figure out how to set this problem up Find the average rate of change f(x)=x^3+1 intervals given [2,3] book says the answer is 19, how do they get that? no matter what I do Im not getting the correct answer.

Mathematics
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\[f(x2)-f(x1)/x2-x1\] \[f(3)-f(2)/3-2\] \[((3)^{3}+1)-((2)^{3}+1)/1\] \[(27+1)-(8+1)\] \[28-9\] \[19\]
we want to find the average rate of change find f'(x)= 3x^2 (df/dx gives the change in f(x) at every instant) now take integral between the limits 2 to 3 Average rate of change= \[1/(3-2) \int\limits_{2}^{3} 3x^2 dx\] \[= 1/1 * [ x^3] \] from 3 to 2 27-8=19
we know that average of a function f(x) in the interval [ a,b] is given by \[1/(b-a) \int\limits_{a}^{b} f(x) dx\]

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